Mathematics I (Calculus) - Syllabus

Definition, domain, and range of functions. Understanding the concept of functions and their representations.

Understanding the graphical representation of functions, including the vertical line test and piecewise defined functions.

Introduction to common functions including linear, power, polynomial, and rational functions.

Shifting and scaling graphs, sums, differences, products, and quotients of functions, and composite functions.

Using calculators and computers to plot graphs of functions.

Definition, exponential behavior, and exponential growth and decay.

Understanding inverse functions and logarithms.

Understanding the rate of change and tangent to curves.

This topic explores the different types of graphs of functions, including their shapes, maxima, and minima, and how to analyze them.

Overview of the development and evolution of the Linux operating system.

Understanding kernel modules, their types, and their role in extending Linux kernel functionality.

Managing processes in Linux, including process creation, synchronization, and termination.

Linux scheduling algorithms and their role in allocating system resources to processes.

Methods and mechanisms for communication between processes in Linux.

Understanding different types of layouts in Android such as Linear, Relative, Table, Absolute, and Constraint layouts.

Learning about various attributes that can be used to customize and configure Android layouts.

Exploring different types of Android widgets such as TextView, EditText, Checkbox, RadioButton, Spinner, and their attributes.

Understanding how to handle events and respond to user interactions in Android applications.

Learning how to work with strings, string arrays, and colors in Android applications.

Understanding how to work with resources and drawables in Android applications.

This topic covers the application of derivatives to sketch curves, including identifying maxima, minima, and inflection points. Students learn to analyze the shape of curves using the first and second derivatives.

This topic reviews the concepts of maxima and minima of one variable functions, including the first and second derivative tests. Students learn to identify and classify local and global maxima and minima.

This topic covers the application of derivatives to solve optimization problems, including finding the maximum or minimum of a function subject to certain constraints. Students learn to model real-world problems and solve them using calculus.

This topic introduces Newton's method for approximating the roots of a function. Students learn to use the method to find the roots of a function and analyze its convergence.

Understanding the different stages of an activity's life cycle, including creation, start, resume, pause, stop, and destroy. This topic covers the methods that are called during each stage.

Learning how to create multiple activities in an Android application, including defining and implementing separate activities for different tasks.

Understanding how to declare activities in the AndroidManifest.xml file, including specifying the activity's name, label, and intent filters.

Learning how to use intents to connect activities, including creating and sending intents, and handling intent requests.

Understanding how to pass data between activities, including using intent extras, bundles, and shared preferences.

Learning how to get a result back from a child activity, including using startActivityForResult() and onActivityResult().

This topic covers the application of derivatives to sketch curves, including identifying maxima, minima, and inflection points. Students learn to analyze the shape of curves using the first and second derivatives.

This topic reviews the concepts of maxima and minima of one variable functions, including the first and second derivative tests. Students learn to identify and classify local and global maxima and minima.

This topic covers the application of derivatives to solve optimization problems, including finding the maximum or minimum of a function subject to certain constraints. Students learn to model real-world problems and solve them using calculus.

This topic introduces Newton's method for approximating the roots of a function. Students learn to use the method to find the roots of a function and analyze its convergence.

This topic explores the concept of finding the surface area of a solid formed by rotating a curve around an axis using antiderivatives.

Understanding the demographics of a society, including population size, density, and distribution, and its impact on social life. This topic explores how population dynamics shape social structures and institutions.

Examining the shared values, beliefs, and practices that define a society, including its norms, customs, and traditions. This topic delves into the role of culture in shaping social behavior and institutions.

Analyzing the social bonds and relationships that form communities, including their characteristics, types, and functions. This topic explores the importance of community in social life.

Understanding the unwritten rules and expectations that govern social behavior, including norms, values, and sanctions. This topic examines how norms and values shape individual and group behavior.

Examining the social positions and expectations associated with different statuses and roles, including their impact on social behavior and relationships. This topic explores the dynamics of status and role in social life.

Analyzing the social structures and relationships within marriage and family institutions, including their functions, types, and changes over time. This topic explores the significance of marriage and family in social life.

Examining the social bonds and relationships based on blood, adoption, or marriage, including their importance in social organization and cultural practices. This topic delves into the role of kinship in social life.

An overview of computers and their significance in today's world. This topic sets the stage for understanding the basics of computers.

Understanding the difference between digital and analog computers, their characteristics, and applications.

Exploring the key characteristics of computers, including input, processing, storage, and output.

A brief history of computers, from their inception to the present day, highlighting key milestones and developments.

Understanding the different generations of computers, including their features, advantages, and limitations.

Categorizing computers based on their size, functionality, and application, including desktops, laptops, and mobile devices.

This topic covers the process of identifying and selecting systems development projects, including corporate and information systems planning.

This topic introduces the process of initiating and planning systems development projects, including assessing project feasibility and building the baseline project plan.

This topic delves into the details of initiating and planning IS development projects, including the process and key activities involved.

This topic covers the importance and process of assessing project feasibility in systems development projects.

This topic explains the process of building and reviewing the baseline project plan in systems development projects.

Definition and properties of normal and binormal vectors, including their applications in physics and engineering.

Motion of objects in space, including velocity, acceleration, and curvature.

Introduction to limits and continuity of functions, including the concept of limits and how they relate to continuity.

Definition and calculation of partial derivatives, including the concept of partial derivatives and their geometric interpretation.

Introduction to tangent planes, including the concept of tangent planes and their relationship to partial derivatives.

Finding maximum and minimum values of functions using partial derivatives, including the concept of critical points and the second partials test.

Introduction to multiple integrals, including the concept of double and triple integrals and their applications.